If cos θ = -4/7, what are the values of sin θ and tan θ?

Solution:

Given, cos θ = -4/7

We have to find the values of sin θ and tan θ.

By trigonometric identity,

cos²θ + sin²θ = 1

So, (-4/7)² + sin²θ = 1

16/49 + sin²θ = 1

sin²θ = 1 - 16/49

sin²θ = (49 - 16)/49

sin²θ = 33/49

Taking square root,

sinθ = √33/7

tanθ = sinθ/cosθ

tanθ = (√33/7) / (-4/7)

tanθ =√33/-4

tanθ = -√33/4

Therefore, the values of sinθ and tanθ are √33/7 and -√33/4.

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If cos θ = -4/7, what are the values of sin θ and tan θ?

Summary:

If cos θ = -4/7, the values of sin θ and tan θ are √33/7 and -√33/4.